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AN   EXPERIMENTAL  STUDY   OF   GROUPING  BY 

SIMILARITY  AS  A  FACTOR  IN  THE 

TEACHING  OF  SPELLING 


Important  Facts  Revealed  by  the  Investigation,  and  Methods  of 
Computation  That  Give  a  Basis  For  Comparative 
Interpretation  of  Results  From  Experi- 
mental Pedagogy,  Are  Also 
Included 


A  Thesis  Presented  to  the  Faculty  of  the  Graduate  School  of 

the  University  of  Pennsylvania  in  part  fulfillment 

of  the  requirements  for  the  Degree  of 

Doctor  of  Philosophy 


BY 


CHARLES  A.  WAGNER 


West  Chester,  Pa. 


AN    EXPERIMENTAL   STUDY   OF   GROUPING  BY 
SIMILARITY  AS  A  FACTOR  IN  THE 
TEACHING  OF  SPELLING 


Important  Facts  Revealed  by  the  Investigation,  and  Methods  of 
Computation  That  Give  a  Basis  For  Comparative 
Interpretation  of  Results  From  Experi- 
mental Pedagogy,  Are  Also 
Included 


A  Thesis  Presented  to  the  Faculty  of  the  Graduate  School  of  the 

University  of  Pennsylvania  in  part  fulfillment  of  the 

requirements  for  the  Degree  of  Doctor  of 

Philosophy 

BY 

CHARLES  A.  WAGNER 
West  Chester,  Pa. 


June  1,  1912 


AN   EXPERIMENTAL  STUDY   OF   GROUPING  BY 

SIMILARITY  AS  A  FACTOR  IN  THE 

TEACHING  OF  SPELLING 

By  Charles  A.  Wagner 
West  Chester,  Pa. 


Ax  Investigation  to  Determine  the  Efficiency  of  Teach- 
ing Spelling  if  the  Words  Be  Grouped  Accord- 
ing to  "Group"  Difficulty  in  Spelling. 

I.     Introduction. 

An  investigation  conducted  by  myself,  for  Doctor  Yocum's 
Seminar  in  Pedagogy,  in  1908,  yielded  the  tentative  conclusion 
that  "Etymology  is  an  effective  help  in  spelling  after  considerable 
of  the  Grammar  of  the  Classical  languages  is  known."  This 
raised  the  question  of  the  effectiveness  for  spelling  of  forms  of 
grouping  other  than  Etymological,  as  phonetic  difficulty,  similar 
silent  letters,  and  so  on. 

The  next  year  an  investigation  of  special  devices  in  spelling, 
such  as  rhymes  or  jingles  for  "ie"  and  "ei"  words,  brought  to 
light  the  existence  of  a  large  number  of  such  devices  among 
educated  people.  This  result  gave  further  impetus  to  the  ques- 
tion, "What  is  the  degree  of  efficiency  of  'group'  association  in 
spelling"  ? 

In  most  instances  spelling  books  have  the  words  arranged  into 
groups.  The  groups  are  either  words  of  the  same  degree  of 
difficulty  or  else  of  names  of  things  "found  in  the  parlor",  "in  the 
attic",  and  so  on.  To  learn  the  names  of  all  the  things  in  the 
parlor  becomes  easy  from  such  a  list,  but  it  is  the  words  and  not 
their  spelling  that  seems  to  be  helped  by  the  grouping,  unless  it 
should  be  found  that  in  some  way  the  recollection  of  the  words 
in  such  a  "contiguous"  list  also  helps  the  spelling  of  these  words. 
The  principle  of  grouping  applied  in  this  experiment  is  the  princi- 
ple of  analogy  or  similarity  of  spelling  difficulty. 

Doctor  J.  M.  Rice,  in  discussing  his  findings  in  his  well-known 
spelling  investigation  in  American  cities,  says  (Forum,  vol.  23, 
page  417)  :  "  .  .  .  the  course  [in  spelling]  is  open  to 
simplification  by  separating  words  that  may  be  learned  collectively 
from  those  that  must  be  learned  individually  .  .  .  That 
little  advantage  is  now  taken  of  rules  in  spelling  is  indicated  by 


2557&9 


the  fact  that,  broadly  spegfcMg,  as  many  errors  were  made  on 
words  governed  by  rules  as  on  Siose  to  which  rules  do  not  apply." 

These  considerations  pointed  the.  way  to  this  investigation. 
What  is  the  measurable  advantage,  under  actual  school  conditions, 
of  teaching  the  spelling  of  words  grouped  according  to  a  common 
difficulty  in  their  spelling?  It  seemed  both  desirable  and  possible 
to  arrange  a  test  to  measure  such  efficiency:  the  selection  of  two 
classes  of  children,  in  the  same  set  of  schools,  alike  in  grading  and 
school  age,  must,  of  course,  be  the  laboratory  in  which  the  test  is. 
to  be  made.  If  one  class  of  children  study  their  spelling  words  in 
the  usual  way,  and  the  other  class  study  the  same  words,  but 
study  them  according  to  groups  on  the  basis  of  similar  difficulty  in 
spelling,  the  difference  of  advantage  one  way  or  the  other  would 
be  likely  to  appear.  The  attempt  was  made,  in  the  experiment, 
to  keep  all  the  conditions  alike,  except  the  spelling  lessons.  In 
one  class  the  source  of  the  words  determined  their  place  in  the  les- 
sons, in  the  other  class,  it  was  the  kind  of  spelling  difficulty  found 
in  the  word.  It  was  also  hoped  that  the  test  might  show  the  rela- 
tive advantages  among  the  kinds  or  groups  of  spelling  difficulty 
selected  in  classifying  the  words  for  the  second  class. 

Does  such  method  tend  to  build  up  a  habit  of  associating  new 
words  with  the  groups  learned?  seemed  another  important  prob- 
lem upon  which  it  was  hoped  some  light  might  be  found.  Be- 
cause such  an  investigation  must  extend  over  years,  it  was  impos- 
sible to  get  any  light  on  the  formation  of  such  a  tendency.  Were 
such  a  tendency  sure  to  follow  from  the  method,  and  there  seems 
much  reason  for  believing  that  it  does,  it  would  be  more  valuable 
than  the  results  found  by  this  investigation.  The  spelling  of  his 
vocabulary  is  not  nearly  so  valuable  to  the  child  as  the  habit  of 
learning  new  words  as  he  encounters  them.  This  is  surely  to  be 
aimed  at  by  all  teaching  of  spelling. 

No  method  is  simple.  All  methods  are  complex,  made  up  of 
many  factors.  When  the  final  method  of  teaching  spelling  is 
formulated,  therefore,  shall  the  grouping  of  words  according  to 
similarity  of  spelling  difficulty  be  one  of  those  factors?  became 
the  final  problem  of  this  study. 

II.     Where  Conducted. 

The  schools  of  a  borough  in  Pennsylvania  with  supervision  by 
the  School  Principal  were  available  for  the  experiment,  and  of- 
fered favorable  conditions.  There  are  two  school  buildings  in 
the  town.  The  buildings  are  about  half  of  the  length  of  the  town 
apart.  This  was  of  advantage  since  it  hindered  the  exchange  of 
experiences  by  the  pupils  in  the  two  classes  while  the  experiment 
was  in  progress.  Each  of  the  buildings  had  a  class  of  sixth 
grade  pupils,  boys  and  girls  in  each  class.  The  teaching  ability 
of  the  teachers  who  had  charge  of  these  rooms  was  rated  as  about 


equal  by  the  Principal,  who  assisted  in  the  conduct  of  the  inves- 
tigation. At  first,  the  intention  had  been  to  include  seventh  and 
eighth  grade  pupils  also,  to  find  if  possible,  how  far  these  older 
children  use  reasoning  power  in  spelling.  In  the  schools  selected 
there  were  no  parallel  grades  seven  and  eight  in  the  two  schools, 
so  this  part  of  the  search  had  to  be  given  up.  Making  deduc- 
tions for  absence  from  the  tests,  in  one  class,  that  which  studied  its 
words  grouped  according  to  likeness  of  spelling  difficulty,  there 
were  twenty-eight  (28)  pupils;  in  t*he  report  this  class  is  called 
Class  A.  In  the  class  which  studied  the  words  in  the  usual  way, 
there  remained  twenty-two  (22)  pupils.  This  class  will  be 
called  Class  B. 

III.     The  Words  Chosen  for  the  Test. 

Two  hundred  words  were  agreed  upon  as  the  test.  A  smaller 
number,  it  was  feared,  might  be  remembered  by  association  by 
contiguity  alone.  That  number  seemed  to  be  enough  to  test  the 
efficiency  of  grouping;  it  would  give  enough  groups  and  would 
permit  of  considerable  variation  in  the  sizes  of  the  groups.  This 
seemed  necessary  to  bring  the  "group''  difficulty  into  active  use 
both  in  learning  and  in  recalling  the  words.  A  larger  number 
would  have  made  a  serious  interference  in  the  regular  work  of 
these  classes  in  their  schools.  Also  it  would  have  required  too 
much  time  to  complete,  and  it  seemed  that  the  work  as  here  plan- 
ned and  described  would  yield  tentative  results  of  value.  If 
grouping  in  study  has  any  efficiency  in  learning  and  recalling  the 
spelling  of  words,  it  seemed  likely  to  appear  as  the  result  of  the 
experiment  as  here  planned,  even  if  larger  and  more  important 
results  must  be  neglected. 

The  words  for  the  test  were  selected  from  the  other  text  books 
studied  by  these  classes.  Their  reader,  history,  geography,  physi- 
ology and  grammar  texts  were  carefully  examined,  and  words 
were  chosen  from  those  parts  of  these  texts  which  had  already 
been  gone  over  that  term.  This  was  done  to  make  sure  of  con- 
tent or  meaning  for  the  words,  and  it  also  made  as  sure  as  condi- 
tions permitted  that  the  words  in  the  spelling  lists  would  not  come 
up  and  be  studied  in  other  lessons  during  the  time  of  the  test. 

For  Class  A,  the  words  were  arranged  into  thirty  (30)  groups, 
each  group  having  the  same  spelling  difficulty.  Then  ten  (10) 
lessons  were  arranged,  each  lesson  containing  from  one  to  three 
words  from  each  of  six  or  eight  of  the  different  groups.  This 
was  done  to  conform  to  the  practice  of  the  school,  twenty  (20) 
words  to  the  spelling  lesson.  In  Class  B  there  were  also  twenty 
(20)  lessons  arranged,  chiefly  according  to  the  order  in  which 
the  words  were  selected  from  the  text  books.  In  the  preliminary 
test  and  in  the  final  test,  the  children  spelled  fifty  (50)  words 


each  dav  for  four  days.     The  total  time  taken  for  the  tests  and 
lessons  was  thus  exactly  twenty  (20)  days,  just  a  school  month. 

IV.  Grouping  the  Words. 

Thirty  bases  of  grouping  were  chosen,  and  the  words  put  into 
the  group  which  seemed  to  represent  the  greatest  difficulty  in  the 
word.  The  smallest  group  had  two  words,  the  largest  had 
sixteen  (16)  words.  With  such  a  small  number  of  words  it  was 
impossible  to  include  all  the  "words  of  like  difficulty  that  might 
belong  to  any  group.  The  method  of  selection  excluded  all 
words  not  found  in  the  text  books,  hence  choosing  from  spellers 
or  dictionaries,  just  to  secure  an  exhaustive  list,  was  precluded. 
It  seems  probable  that  the  group  containing  the  group  difficulty 
called  the  "line"  group,  Group  one,  approaches  very  closely  to 
containing  all  the  words  commonly  used.  The  words  them- 
selves and  the  grouping,  as  well  as  the  "group"  difficulties 
selected,  will  all  be  shown  in  the  table  of  results,  and  are  there- 
fore omitted  here. 

The  continuous  repetition  of  the  "group"  difficulty,  as  provided 
in  the  lessons  for  Class  A,  seemed  necessary,  to  secure  the  highest 
possible  degree  of  certainty  that  the  "group"  difficulty  should  be 
learned,  that  the  words  in  the  group  should  be  associated  with  it, 
and  so  that  dependence  upon  it  should  have  a  chance  to  develop. 
It  is  believed,  for  instance,  that  to  have  learned  all  the  words  of  a 
few  groups  as  a  single  lesson,  and  not  to  have  repeated  the  group 
after  that,  would  have  afforded  a  mimimum  chance  for  any  ad- 
vantage of  grouping  to  show  itself.  To  train  the  child  to  depend 
upon  grouping,  he  must  use  grouping  frequently,  so  that  "groups 
analogy  shall  function  certainly  and  quickly. 

V.  Preliminary  Test. 

A  preliminary  test  was  decided  upon  as  a  basis  from  which  to 
measure  the  improvement  of  each  class.  Both  classes  were  given 
the  entire  list  of  two  hundred  (200)  words  to  spell,  in  lessons  of 
fifty  (50)  words  each,  without  any  fresh  study  of  them.  The 
results  attained  in  this  test  are  the  basis  from  which  improvement 
is  reckoned.  The  regular  teachers  conducted  these  tests.  The 
children  were  not  told  what  was  in  progress,  except  that  it  was 
review  work  in  spelling.  This  probably  secured  normal  condi- 
tions and  the  children's  best  effort.  Only  the  results  for  the 
classes  as  a  whole  are  shown.  In  the  report  to  the  Seminar,  no 
difference  by  sexes  was  noticeable,  hence  they  are  here  omitted.. 

VI.  Metdod  of  Presentation  or  Teaching  the  Words. 

After  the  preliminary  test,  actual  study  of  the  entire  list  of 
words,  was  begun  by  each  class.  ///  Class  A,  the  "grouping" 
class,  each  word  of  a  twenty  (20)  word  lesson  was  written  upon 


the  black-board  by  the  teacher.  If  any  child  could  use  the  word 
in  a  sentence  or  give  its  meaning-  so  that  the  entire  class  under- 
stood, then  the  class  was  assumed  to  know  the  meaning*  of  the 
word.  If  no  child  could  tell  its  meaning,  the  teacher,  by  sug- 
gestion or  hint,  tried  to  recall  the  connection  where  the  class  had 
met  the  word,  and  thus,  if  possible,  secured  the  recall  of  a  mean- 
ing already  learned.  Meaning,  or  content  for  the  word,  even  if 
but  partial,  being  thus  assured,  each  of  the  following  steps  was 
taken  if  the  learning  of  groups  had  gone  ahead  far  enough  to 
require  it : 

(  i  )    To  which  group  of  our  list  may  this  word  be  added? 
( 2  )    What  words  have  we  already  learned  that  will  help  us 

to  remember  this? 
(  3  )    Name  all  the  words  already  learned  that  will  help  you 

to  remember  this  one? 

Then  each  word  was  written  two  times,  to  conform  to  the  regu- 
lar practice  of  this  class  and  teacher. 

In  Class  B,  the  proceeding  was  the  same  while  making  sure 
that  the  words  had  meaning  or  content.  Then  some  pupil  was 
asked  to  point  out  the  hard  part  of  the  word,  or  the  place  where 
one  would  be  likely  to  make  a  mistake  in  spelling.  Some  likely 
mistake  was  always  found.  Had  the  teacher  been  instructed  to 
point  out  the  difficulty  for  the  children,  it  was  feared  that  stress 
might  be  put  upon  the  same  difficulty  in  both  classes.  The  results 
seem  to  show  that  the  class  that  studied  its  words  in  ordinary  lists 
yet  hit  upon  group  spelling  difficulty  as  the  "hard  part"  of  the 
word. 

Xext  each  word  was  written  three  times,  to  conform  with  the 
usual  custom  of  this  class  and  teacher.  In  both  classes  this  so- 
called  writing  the  words  means  the  writing  of  each  word  in  imme- 
diate succession.  Should  the  writing  of  the  words  two  times  in 
one  class  and  three  times  in  the  other  be  regarded  as  a  serious 
variation  ?  Since  it  was  Class  B  that  wrote  them  oftener,  and 
since  it  was  Class  A  that  was  trying  the  "grouping,"  it  seemed 
clear  that  whatever  advantage  there  might  be  in  the  three  writ- 
ings, must  accrue  to  the  Class  B,  which  studied  its  words  in  the 
ordinary  groups.  Therefore  this  conformity  to  usual  school  con- 
ditions seemed  better :  it  gave  the  children  no  chance  to  become 
curious  or  suspicious  that  something  unusual  was  going  on. 
Normal  states  of  mind  and  attitude  toward  the  work  were  thus 
secured  and  maintained.  Since  favorable  results,  if  any,  would 
be  against  "grouping"  rather  than  in  favor  of  it,  the  variation  is 
here  mentioned  merely  as  an  explanation,  not  with  the  belief  that 
it  caused  any  disturbance  whatever  in  the  results. 


VII.  The  Spelling  Lessons. 

All  spelling  lessons,  and  all  the  test  exercises,  were  given  in  the 
first  period  of  the  afternoon  session  of  the  school,  between  1.45 
and  2.15  p.m.  The  first  ten  minutes  were  given  to  the  pre- 
sentation of  the  words  after  the  plan  already  described.  Then 
followed  the  writing  of  the  words — the  study :  for  this  study  or 
writing,  twenty  minutes,  or  as  much  of  it  as  was  needed,  was 
given  to  the. writing  or  practicing  from  the  black-board  copy. 
Then  the  lesson  of  twenty  words  was  pronounced  to  be  spelled 
in  the  usual  way.  All  papers  were  then  collected.  The  teachers 
and  the  investigators  marked  the  papers.  Papers  were  not  re- 
turned to  the  children. 

Each  teacher  noted  the  words  misspelled  in  the  lessons.  When 
the  entire  list  of  words  had  been  studied  and  spelled,  these  lists  of 
misspelled  words  were  treated  as  two  new  lessons,  each  word  be- 
ing again  presented  as  if  it  were  a  new  word.  The  papers  of  the 
review  lessons  were  not  kept,  the  errors  were  not  counted,  and  no 
record  of  them  is  included  here.  Since  each  class  of  children 
gave  extra  study  to  those  words  which  appeared  more  difficult,  it 
seems  permissible  to  omit  this  phase  of  the  work.  The  mis- 
spelled words  were  restudied  to  conform  to  the  practice  of  the 
school.  This  variation  told  against  Class  B  if  it  made  any  dif- 
ference, since  that  class  missed  the  larger  number  of  words  in  the 
daily  lessons.  Probably  this  difference  is  so  slight  as  to  be  en- 
titled to  mention  only  and  not  to  actual  consideration  or  computa- 
tion. 

VIII.  Marking  and  Counting  Errors. 

Two  classes  of  errors  were  arranged  as  the  basis  for  tabulation 
and  comparison.  Misspelling  of  any  kind  made  a  word  wrong. 
Next,  words  that  were  wrong  were  examined  for  the  kind  of  mis- 
take or  mistakes  that  had  been  made.  Any  error  due  to  not 
knowing  or  not  using  the  "group"  difficulty  was  called  a  group 
error.  All  other  kinds  of  errors,  such  as  omitted  letters,  wrong 
letters,  and  so  on,  were  called  "non-group"  errors.  For  instance, 
the  word  "conscience,"  if  written  "consience,"  was  counted  wrong 
and  the  error  was  regarded  a  "grouping"  error;  if  written 
"consciense,"  the  error  was  called  a  "non-grouping"  error.  This 
classification  of  errors  furnished  the  basis  for  determining  the  ef- 
fectiveness of  "grouping"  in  eliminating  "group"  errors,  and 
also  for  the  comparison  of  the  groups  as  to  relative  efficiency. 

There  were,  of  course,  many  more  errors  than  misspellings : 
that  is,  some  words  had  several  mistakes  in  them,  some  having  as 
many  as  four  errors  in  the  preliminary  test.  In  computing  the 
class  standing,  only  the  number  of  misspelled  words  was  counted. 
In  computing  the  efficacy  of  the  groups  and  of  the  grouping,  the 
number  of  errors  wras  also  included. 

8 


In  marking  the  words,  the  singular  difficulty  came  to  light  that 
some  words  might  with  equal  propriety  be  included  under  several 

ups"  of  difficulty.  Thus  "conception."  although  actually  in- 
eluded  in  the  etymological  group,  might  also  have  been  included 
in  the  "group"  "tion  as  shun."  In  such  cases,  the  error  was 
counted  as  a  grouping  error  if  the  "group"  difficulty  under  which 
the  word  was  studied  was  not  used  in  the  spelling.  Thus,  an 
error  resulting  from  not  remembering  "cept"  as  the  group  diffi- 
culty for  "conception,"  was  regarded  as  a  group  error,  and  any- 
thing else  in  this  word  as  a  non-group"  error.  Words  omitted 
in  the  les  r  tests  by  any  pupils,  or  words  substituted  for 

those  pronounced  by  the  teacher  were  all  counted  as  "non-group- 
ing" errors. 

The  group  of  words  ending  in  "y"  in  the  singular  seems  to  pre- 
sent no  group  difficulty;  in  the  plural  the  rule  for  spelling  "y" 
plurals  was  used,  so  that  rules  of  spelling,  as  suggested  by  Rice, 
have  had  a  small  trial  here. 

Many  perplexing  decisions  had  to  be  made  in 'marking  the 
papers  and  in  classifying  the  errors.  "Graphophone"  was  most 
frequently  misspelled  by  writing  it  "graphone."  It  had  been 
grouped  with  the  "graph"  words :  the  "graph"  is  present,  but 
shall  we  call  it  a  grouping  or  a  non-grouping  error?  Did  the 
child  write  "graph  one"  or  "gra  phone"  ?  As  the  words  had  not 
been  written  in  syllables,  we  could  not  tell  absolutely.     For  safe- 

-ake — to  avoid  the  suspicion  of  trying  to  make  out  a  case  for 
the  experiment — all  such  errors  were  counted  as  non-grouping. 
Only  clear  and  unmistakable  cases  of  ignorance  or  non-use  of  the 

up"  difficulty  were  counted  "grouping"  errors:  all  others 
were  counted  as  "non-grouping." 

IX.  Marking  the  Papers. 

First  the  teachers  marked  the  papers :  then  the  investigators 
looked  them  over,  confirmed  the  markings,  and  classified  the 
errors.  Then  the  counts  were  taken.  This  precaution  seemed 
best  to  guard  against  any  disposition  to  find  errors  in  favor  of  the 
test,  namely,  "group"  errors.  In  the  tables  of  results,  the 
•uping  errors"  are  called  "g"  errors,  and  the  "non-grouping" 
enors  are  called  "ng"  errors. 

X.  Results. 

For  convenience  of  all  kinds,  the  figures  for  both  tests  are 
placed  side  by  side  in  the  tables.  The  words  are  there  arranged 
into  groups  as  they  were  listed  for  the  "grouping"  class,  under 
their  respective  "group"  headings.  The  table  is  intended  to 
show  just  what  were  the  results  for  each  word,  for  each  group  of 
w«  »rds.  and  for  each  class,  in  lxjth  tests. 


The  results  of  the  daily  spelling  lessons  do  not  appear  in  the 
table.  For  the  sake  of  completeness,  they  are  stated  here.  Class 
A,  28  pupils,  missed  a  total  of  100,  words,  during-  the  time  of  daily 
iessons.  Class  B,  in  the  same  time,  missed  no  words,  but  it  had 
only  22  pupils.  The  average  for  Class  A  is  thus  3.9  words  per 
pupil  for  the  ten  lessons,  and  for  Class  B  it  is  5  words  per  pupil. 
In  the  preliminary  test,  it  will  be  noticed,  that  Class  A  had  the 
poorer  showing,  so  that  this  difference  at  once  becomes  a  differ- 
ence in  favor  of  the  "grouping"  here  tried. 

The  attendance  of  the  pupils  during  the  time  of  the  lessons  was 
as  follows: 

Class  A  :  3  pupils  absent  for  one  lesson  each,  2  pupils  absent  for 
2  lessons  each,  and  2  pupils  absent  for  4  days  each,  a  total  of  15 
days.. 

Class  B :  4  pupils  absent  for  1  day  each,  and  one  pupil  absent  2 
days,  a  total  of  6  days. 

Class  A  thus  was  present  less  that  91%  of  the  learning  time, 
and  Class  B  was  present  nearly  98%  of  that  time.  Class  A,  the 
"grouping"  class,  made  the  poorer  showing  at  the  start,  was 
present  a  smaller  percentage  of  the  learning  time,  yet  it  made 
the  better  showing  in  the  lessons.  As  an  indication  this  differ- 
ence is  entitled  to  statement  here. 

Since  each  class  had  two  days  of  review,  and  since  the  reviews 
are  not  counted  in  the  results  of  the  daily  lessons,  it  is  only  the 
trend  of  the  lessons  that  may  be  summarized. 

Tabulation  of  results,  showing  misspellings  and  numbers  of 
the  several  kinds  of  errors : 


CLASS 

A. 

CLASS  B. 

(GROUPING  METHOD  OF  STUDY.) 
28  Pupils  in  Class. 

(NON-GROuPING  METHOD   OF   STUDY.) 
22  Pupils  in  Class. 

MISSPELLINGS 

ERRORS 

MISSPELLINGS 

ERRORS 

Prelim.  Final               Grouping 
Test.    Test.               Prel.    Fin. 

Non-grouping 
Prel.      Fin. 

Prelim. 
Test. 

Final 
Test. 

Grouping 
Prel.    Fin. 

Non-grouping 
Prel.      Fin. 

GROUP  1,   ' 

'line"  as  base 

;  4  words: 

15           1 
18           1 

7 
16 

1 

1 

10 
11 

0 
0 

lineage 
lineal 

11 

13 

0 
1 

8 
12 

0 
0 

5 

4 

0 
1 

21            2 

12 

1 

15 

1 

lineament 

18 

3 

12 

1 

10 

o 

24            0 

19 

0 

14 

0 

linear 

18 

1 

12 

0 

12 

1 

78            4 

54 

3 

50 

1 

60 

5 

41 

1 

21 

4 

GROUP  2,   ' 

'que"  as  k;  6  words 

25            1 

21 

0 

21 

1 

arabesque 

22 

3 

22 

1 

14 

2 

26            0 
4            0 
1            1 

25           1 

18           7 

25 

2 

1 

25 

14 

0 
0 
0 
0 
6 

12 
3 
0 
3 
4 

0 

0 

1 
1 

4 

grotesque 
oblique 

opaque 

picturesque 

pique 

18 
9 
12 
13 
13 

3 
0 
3 
1 

4 

16 
4 
11 
11 
10 

0 
0 

1 

0 

1 

12 
6 
5 
5 

13 

3 
0 
2 
2 
3 

99          10 

88 

6 

43 

7 

87 

14 

74 

3 

55 

12 

GROUP  3,   ' 

'verd"  as  green,  as  base;  4  words: 

21            2 
19            1 

3 
15 

0 
1 

20 
6 

2 
0 

Cape  Verde 
verdant 

14 

0 
5 

4 

1 

0 
5 

13 

0 
0 

20            5 

12 

5 

16 

1 

verdure 

13 

2 

9 

2 

6 

0 

4            1 

0 

0 

4 

1 

Vermont 

11 

4 

(I 

0 

1 

4 

IO 


CLASS  A. 

(GROUPING  METHOD   OF  STUDY.) 

28  Pupils  in  Class. 

MISSPELLINGS  ERRORS 

Prelim.  Final  Grouping       Non-grouping 

Test.     Test.  Prel.    Fin.      Prel.      Fin. 

GROUP  4,   "ch"  as  k;  11  words: 


CLASS  B. 
(NON-GROUPING  METHOD  OF  STUDY.) 

22  Pupils  in  Class. 
MISSPELLINGS  ERRORS 

Prelim.  Final  Grouping       Non-grouping 

Test.    Test.  Prel.     Fin.      Prel.      Fin. 


24 

1 

24 

0 

24 

1 

catechism 

18 

4 

14 

1 

20 

4 

■22 

2 

19 

0 

16 

2 

chasm 

14 

2 

11 

0 

14 

2 

7 

0 

3 

0 

5 

0 

chemist 

3 

1 

1 

0 

3 

1 

28 

5 

27 

4 

28 

5 

choleric 

21 

5 

20 

4 

18 

4 

21 

0 

21 

0 

6 

0 

chord 

12 

2 

11 

2 

5 

0 

1 

0 

1 

0 

1 

0 

chorus 

5 

1 

1 

0 

4 

1 

16 

2 

2 

0 

16 

2 

Christian 

4 

6 

0    ■ 

0 

4 

6 

5 

0 

0 

0 

5 

0 

Christmas 

2 

0 

1 

0 

2 

0 

19 

4 

8 

1 

27 

4 

chrysalis 

21 

4 

15 

2 

22 

2 

9 

1 

8 

0 

4 

1 

monarch 

8 

0 

8 

0 

0 

0 

24 

6 

18 

3 

16 

4 

patriarch 

14 

1 

12 

0 

8 

2 

176 

21 

131 

8 

148 

19 

122 

26 

94 

9 

100 

22 

GROUP 

5,   "ci 

."  as  sound 

of  sh; 

4  words 

25 

1 

17 

1 

14 

0 

capacious 

16 

2 

11 

0 

11 

2 

17 

0 

14 

0 

12 

0 

ferocious 

13 

2 

7   : 

1 

14 

1 

1 

1 

0 

0 

1 

1 

precious 

o 

0 

0    : 

0 

3 

0 

19 

5 

10 

4 

16 

3 

vicious 

14 

2 

8 

1 

9 

1 

41 


GROUP  6,   "geon"  as  jon;  5  words: 


37 


23 

1 

23 

1 

10 

0 

bludgeon 

21 

3 

16 

1 

12 

0 

19 

0 

19 

0 

12 

0 

dungeon 

10 

0: 

9 

0 

5 

0 

3 

1 

3 

0 

1 

1 

pigeon 

1 

1 

1 

0 

0 

1 

16 

6 

5 

2 

15 

6 

surgeon 

15 

1 

6 

0 

12 

1 

12 

1 

7 

1 

±1 

1 

sturgeon 

6 

1 

5 

0 

6 

1 

78 


57 


19 


GROUP  7,  "tyr"  as  ter;  3  words: 
11  2  9  2  3 

4  1  4  0  1 


27 


25 


37 


35 


0 

martyr 

3 

0 

1 

0 

2 

0 

1 

martyrdom 

4 

1 

1 

0 

4 

1 

1 

satyr 

22 

13 

21 

12 

5 

4 

73 


46 


23 


12 


GROUP  8,   ' 

'ti"   as  sh;  6 

words : 

27 

0 

22 

0 

11 

0 

insatiate 

19 

5 

19 

4 

11 

1 

20 

1 

0 

1 

20 

0 

martial 

13 

2 

12 

2 

5 

2 

15 

0 

10 

0 

12 

0 

partial 

12 

1 

8 

1 

6 

1 

4 

0 

1 

0 

4 

0 

patience 

3 

1 

0 

0 

3 

1 

1 

1 

0 

0 

1 

1 

patient 

3 

0 

0     . 

0 

3 

0 

7 

1 

3 

1 

5 

0 

quotient 

5 

0 

4 

0 

4 

0 

74 

3 

36 

2 

56 

1 

55 

9 

43 

7 

32 

5 

GROUP 

9, 

"ant"  as  ent; 

7  words: 

27 

(> 

10 

0 

27 

0 

buoyant 

21 

6 

8 

0 

18 

16 

7 

1 

6 

1 

3 

1 

claimant 

1 

2 

1 

2 

0 

0 

6 

2 

5 

1 

2 

1 

gallant 

10 

0 

7 

0 

8 

0 

9 

3 

9 

2 

0 

1 

informant 

8 

2 

8 

2 

1 

6 

3 

0 

2 

0 

1 

0 

radiant 

2 

1 

0 

0 

2 

1 

12 

0 

8 

0 

8 

0 

tenant 

11 

3 

5 

1 

6 

2 

21 

0 

10 

0 

17 

0 

truant 

8 

3 

5 

3 

4 

2 

85 

6 

50 

4 

58 

3 

61 

17 

34 

8 

39 

11 

GROUP 

10, 

"cept"  as  base;  6  words: 

11 

0 

0 

0 

11 

0 

accept 

4 

2 

1 

0 

3 

2 

22 

2 

18 

2 

5 

0 

conception 

16 

6 

16 

5 

3 

1 

7 

1 

3 

0 

4 

1 

exception 

2 

0 

1 

0 

1 

0 

16 

2 

11 

0 

6 

2 

intercept 

5 

4 

4 

4 

1 

0 

7 

0 

7 

0 

2 

0 

precept 

4 

1 

4 

0 

1 

1 

10 

0 

7 

0 

4 

0 

reception 

3 

1 

3 

0 

0 

1 

II 


CLASS  A 
(GROUPING  METHOD  OF  STUDY.) 

28  Pupils  in  Class. 
MISSPELLINGS  ERRORS 

Prelim.  Final  Grouping      Non-grouping 

Fin. 


CLASS  B 

(NON-GROUPING  METHOD   OF   STUDY.) 

22  Pupils  in  Class. 


Test. 

Teat. 

GROUP 

11, 

15 

1 

3 

2 

26 

3 

4 

3 

10 

0 

5 

1 

16 

0 

10 

0 

89 

10 

GROUP 

12, 

15 

3 

8 

0 

1 

0 

8 

0 

13 

1 

28 

2 

7 

1 

20 

1 

1 

0 

1 

0 

Prel.    Fin.      Prel. 
'ph"  as  f;  8  words: 


15 


"graph'  as  base;  10  words: 


MISSPELLINGS 

Prelim.  Final 

Test.    Test. 


cipher 

elephants 

phalanx 

phantom 

physic 

sulphur 

sapphire 

triumph 


autograph 

biography 

geography 

graphic 

graphite 

graphophone 

paragraph 

phonograph 

photograph 

telegraph 


ERRORS 
Grouping      Non-grouping 
Prel.    Fin.      Prel.      Fin. 


0 

1 

7 

1 

0 

0 

4 

0 

0 

0 

0 

0 

8 

0 

0 

0 

9 

1 

8 

1 

4 

1 

14 

0 

1 

0 

2 

1 

0 

0 

3 

1 

1 

0 

2 

1 

0 

0 

0 

0 

102           2  23           1           90           8 

GROUP  13,  "gyp"  as  jip;  3  words: 

12  0           0             12 

27            2  3            0            26           2 

10  0            0              10 


Egypt 

gypsum 

gypsy 


40 


GROUP  14, 
4  1 

6  0 

0 

0 
2 
2 
1 

0 


3  0 

as  s;  8  words: 
2  1 


GROUP  15, 
26  0 


51  4 

V*  silent:  5  words: 


37 


descent 

fascinate 

scenic 

scenery 

scepter 

science 

scissors 


aghast 

dahlia 

honest 

rhubarb 

shepherd 


J  0 


48  2 

GROUP  16, 


39  0  21 

'eigh"  as  long  a;  5  words: 
28  0  3 


0  3 

0  0 

0  0 

0  0 


inveigh 

neigh 

neighbor 

sleigh 

weight 


44  0 

GROUP  17, 

10  0 


43  0  6 

'mission"  as  base;  6  words: 


84 


admission 

mission 

intermission 

missionary 

permission 

remission 


50 


42 


14 


12 


U 


10 


CLASS  A. 

(GROUPING  METHOD   OF  STUDY.) 
28  Pupils  in  Class. 
MISSPELLINGS  ERRORS 


CLASS  B. 

(NON-GROUPING  METHOD   OF   STUDY.) 
22  Pupils  in  Class. 
MISSPELLINGS  ERRORS 


Prelim. 

Final 

Grouping 

Non- grouping 

Prelim. 

Final 

Grouping 

Non-grouping 

Test. 

Test. 

Prel. 

Fin. 

PreL 

Fin. 

Test. 

Test 

PreL 

Fin. 

PreL 

Fin. 

GROUP 

'  18,  "y" 

preceded  by  a 

constant, 

plural 

nouns;    9  words: 

7 

0 

5 

0 

2 

0 

canaries                 7 

1 

5 

1 

2 

0 

6 

2 

5 

1 

5 

2 

canopies                 7 

4 

3 

2 

4 

2 

2 

1 

0 

0 

2 

1 

colonies                 2 

0 

1 

0 

1 

0 

7 

1 

3 

0 

4 

2 

deliveries              6 

0 

2 

0 

4 

0 

18 

1 

3 

0 

15 

1 

quantities             8 

1 

2 

0 

6 

1 

13 

3 

5 

0 

8 

3 

securities              9 

1 

7 

0 

2 

1 

2 

0 

2 

0 

0 

0 

stories                     1 

0 

1 

0 

0 

0 

16 

1 

7 

0 

12 

1 

tapestries             13 

0 

9 

0 

f 

0 

2 

0 

0 

0 

2 

0 

tributaries             2 

1 

0 

0 

2 

1 

30 


00 


10 


GROUP  19,  "ie"  as  long  e;  10  words: 


6 

4 

1 

0 

23 

1 

3 

0 

7 

1 

4 

2 

1 

0 

3 

0 

26 

2 

5 

4 

1 

0 

believe 

0 

0 

1 

0 

chief 

11 

1 

19 

0 

fiend 

2 

0 

1 

0 

fierce 

5 

1 

2 

1 

grieve 

2 

1 

2 

1 

piece 

0 

0 

1 

0 

pierce 

2 

0 

1 

0 

thief 

26 

2 

24 

0 

wield 

77 


10 


6B 


GROUP  20,  "scio,"  to  know,  as 
5  1  2  0 

SO  4  0 


base;  2  words: 

4  2        conscience 

6  0        conscious 


13 


10 


2 


40 


14 


4 

3 

.    0 

0 

1 

1 

0 

0 

4 

1 

1 

1 

1 

1 

1 

0 

4 

1 

2 

0 

3 

3 

3 

0 

3 

1 

0 

0 

2 

1 

0 

0 

L0 

1 

13 

2 

34 


GROUP  21,  singular  "y"  preceded  by  a  consonant  nouns  (no  grouping  for  these);  9  words: 


58  8 

GROUP  22, 

12  0 

6  0 
4  0 

7  0 
1  0 


0  0  60 
'ea"  as  long  e;  5  words: 

4  0  9 

5  0  6 
0  0  4 

6  0  2 
0  0  1 


canary 

canopy 

colony 

delivery 

quantity 

security 

story 

tapestry 

tributary 


bereave 

eager 

easel 

fearful 

weasel 


20 


10 


0 

0 

4 

1 

0 

0 

2 

0 

0 

0 

1 

2 

0 

0 

0 

1 

0 

0 

9 

2 

0 

0 

0 

1 

0 

0 

1 

1 

0 

0 

5 

0 

0 

0 

2 

1 

— 

—i 

— 

0 

0 

24 

9 

L4 

2 

1 

0 

2 

0 

2 

0 

0 

0 

5 

1 

1 

1 

4 

0 

0 

0 

1 

0 

15 


GROUP  23,   "tion"  as  shun;  12  words: 


27 


07 


21 


17 


13 


8 

2 

0 

0 

8 

2 

affliction 

7 

5 

0 

0 

7 

5 

9 

0 

4 

0 

8 

0 

completion 

1 

0 

1 

0 

0 

0 

0 

0 

0 

0 

0 

0 

direction 

0 

0 

0 

0 

0 

0 

5 

0 

0 

0 

5 

0 

exertion 

4 

2 

2 

1 

2 

1 

21 

1 

0 

0 

21 

1 

irrigation 

18 

10 

1 

0 

23 

11 

1 

0 

0 

0 

1 

0 

objection 

0 

0 

0 

0 

0 

0 

3 

0 

1 

0 

3 

0 

observation 

1 

1 

0 

0 

1 

1 

0 

0 

0 

0 

0 

0 

perfection 

1 

0 

0 

0 

1 

0 

3 

1 

1 

0 

2 

1 

reflection 

1 

0 

0 

0 

1 

0 

13 

2 

1 

0 

15 

2 

suffocation 

2 

1 

0 

0 

2 

1 

3 

0 

0 

0 

3 

0 

transaction 

2 

0 

0 

0 

2 

0 

1 

0 

0 

0 

1 

0 

vegetation 

4 

2 

0 

0 

4 

2 

43 


13 


CLASS 

A. 

CLASS  B. 

(GROU 

(NOj 

28 

Pupils  in 

i  Class. 

22  Pupils  in 

Class. 

MISSPELLINGS 

ERRORS 

MISSPELLINGS 

ERRORS 

Prelim. 

Final 

Grouping      Non-grouping 

Prelim, 

.  Final 

Grouping 

Non-grouping 

Test. 

Test. 

Prel. 

Fin. 

Prel. 

Fin. 

Test. 

Test. 

Prel. 

Fin. 

Prel. 

Fin. 

GROUP 

24,   "1" 

silent;  9 

words : 

G 

-  0 

5 

0 

2 

.  0 

almond 

6 

1 

5 

1 

5 

1 

7 

•0 

3 

0 

6 

0 

balky 

3 

0 

1 

0 

2 

0 

2 

1 

0 

0 

2 

1 

calm 

2 

0 

0 

0 

2 

0 

0 

•0 

0 

0 

0 

0 

chalk 

2 

0 

0 

0 

2 

0 

r4 

0 

1 

0 

4 

0 

embalm 

2 

0 

2 

0 

0 

0 

6 

n 

0 

0 

6 

0 

Lincoln 

2 

0 

1 

0 

1 

0 

1 

0 

0 

0 

1 

0 

palm 

1 

1 

0 

0 

1 

1 

(15 

r.i 

1 

1 

15 

0 

psalm 

9 

1 

1 

0 

8 

1 

5 

0 

2 

0 

4 

0 

salmon 

4 

2 

3 

0 

3 

2 

46 

2 

12 

1 

40 

1 

31 

5 

13 

1 

24 

5 

GROUP 

26,   "dg 

"  as  j;  16 

i  words: 

3 

0 

1 

0 

3 

0 

acknowledge 

0 

0 

0 

0 

0 

0 

6 

0 

5 

0 

4 

0 

begrudge 

3 

2 

3 

1 

1 

1 

:2 

0 

0 

0 

2 

0 

bridge 

0 

0 

0 

0 

0 

0 

13 

0 

5 

0 

12 

0 

cartridge 

9 

1 

7 

0 

7 

1 

11 

0 

6 

0 

7 

0 

dodge 

0 

1 

0 

0 

0 

1 

■7 

0 

3 

0 

5 

0 

drudge 

4 

1 

2 

0 

4 

1 

1 

0 

0 

0 

1 

0 

fledge 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

fudge 

1 

1 

1 

0 

0 

1 

5 

0 

1 

0 

5 

0 

grudge 

1 

0 

1 

0 

0 

0 

2 

0 

0 

0 

2 

0 

hedge 

2 

0 

0 

0 

2 

0 

8 

0 

1 

0 

7 

0 

knowledge 

3 

1 

1 

1 

3 

0 

5 

1 

1 

1 

5 

1 

ledger 

1 

2 

1 

1 

1 

1 

4 

0 

2 

0 

2 

0 

pledge 

1 

0 

0 

0 

1 

0 

1 

0 

0 

0 

1 

0 

ridge 

1 

0 

0 

0 

1 

0 

1 

0 

1 

0 

0 

0 

sledge 

1 

0 

0 

0 

1 

0 

5 

0 

3 

0 

3 

0 

wedge 

1 

0 

0 

0 

1 

0 

74 

1 

29 

1 

59 

1 

28 

9 

16 

3 

22 

6 

GROUP 

27,   "gh 

"  silent; 

7  words 

2 

1 

0 

0 

2 

1 

bough 

1 

0 

1 

0 

1 

0 

0 

0 

0 

0 

0 

0 

blight 

1 

0 

1 

0 

0 

0 

15 

1 

0 

0 

15 

1 

haughtily 

7 

4 

3 

0 

7 

4 

9 

0 

2 

0 

9 

0 

plight 

2 

0 

1 

0 

2 

0 

2 

1 

0 

0 

2 

1 

thought 

1 

3 

0 

0 

1 

3 

0 

0 

0 

0 

0 

0 

through 

0 

1 

0 

0 

0 

1 

1 

0 

0 

0 

1 

0 

tight 

0 

0 

0 

0 

0 

0 

29 

3 

2 

0 

29 

3 

12 

8 

6 

0 

11 

8 

GROUP 

25,   "n" 

silent;  5 

words : 

2 

0 

0 

0 

2 

0 

autumn 

0 

1 

0 

1 

0 

0 

4 

4 

0 

0 

4 

4 

column 

8 

5 

4 

0 

8 

6 

10 

1 

10 

1 

1 

0 

condemn 

9 

3 

9 

3 

2 

1 

2 

.0 

1 

0 

1 

0 

hymn 

0 

0 

0 

0 

0 

0 

6 

1 

2 

0 

6 

1 

solemn 

8 

3 

3 

0 

6 

4 

24 


13 


14 


2fi 


GROUP  28,  "ern"  meaning  direction;  4  words: 

10  0           0             10        eastern 

3           0  10             2            0        northern 

2           0  0            0             2            0        southern 

1          .1  10             11        western 


12 


GROUP  29, 

"gh" 

as  f; 

5  words: 

1            0 

1 

0 

0 

0 

enough 

0 

1 

0 

0 

0 

1 

0            0 

0 

0 

0 

0 

laugh 

0 

0 

0 

0 

0 

0 

1             0 

1 

0 

0 

0 

rough 

4 

1 

3 

0 

3 

1 

2            0 

0 

0 

2 

0 

slough 

2 

0 

1 

0 

2 

0 

3            1 

1 

0 

2 

1 

tough 

2 

0 

0 

0 

2 

0 

u 


CLASS  A. 

(GROUPING  METHOD   OF  STUDY.) 
28  Pupils  in  Class. 


CLASS  B. 

(NON-G*,~dPING  METHOD    OF   STUDY.) 
22  Pupils  in  Class. 


MISSPELLINGS 

ERRORS 

MISSPELLINGS 

ERRORS 

Prelim.  Final 

Grouping 

Xi  in-grouping 

Prelim. 

Final 

Grouping 

Non-grouping 

Test.    Test. 

Prel. 

Fin. 

Prel. 

Fin. 

Test. 

Test. 

Prel. 

Fin. 

Prel. 

Fin. 

GROUP  30,   • 

head' 

'  as  base;  6  words: 

0           0 

0 

0 

0 

0 

behead 

0 

1 

0 

0 

0 

1 

0            0 

0 

0 

0 

0 

deadhead 

0 

1 

0 

0 

0 

1 

0             1 

0 

0 

0 

1 

forehead 

1 

0 

0 

0 

1 

0 

1            0 

0 

0 

1 

0 

headache 

1 

0 

0 

0 

1 

0 

3            0 

0 

0 

3 

0 

headlong 

0 

0 

0 

0 

0 

0 

4            1 

0 

0 

4 

1 

hogshead 

5 

2 

1 

1 

5 

1 

SUMMARIES  BY   GROUPS. 


No.  of 
GROUPS.       words 
in  gr'p. 

1.  line   4 

2.  que    6 

3.  verd    4 

4.  "oh"     11 

5.  "ci"    4 

6.  geon   5 

7.  tyr     3 

8.  "ti"    6 

9.  ant    7 

10.  eept    6 

11.  "ph"    8 

12.  graph   10 

13    gyp    3 

14.  "sc"    8 

15.  "h"     .......     5 

16.  eigh    5 

17.  sion     6 

18.  ies  plur.   ..     9 

19.  "ie"     10 

20.  scio     2 

21.  "y"  sing...     9 

22.  "ea"    5 

23.  tion    12 

24.  "1"    9 

25.  "n"     5 

26.  "dg"    16 

27.  "gh"    7 

28.  em    4 

29.  "gh"     (f)..     5 

30.  head    6 


CLASS  A,  28  Pupils. 

Words  Errors, 

Missed.  Grouping.    Non-gr'ping. 

Prel.       Fin.  Prel.      Fin.      Prel.    Fin. 


CLASS 

Words 

Missed. 

Prel.      Fin. 


B,   22  Pupils. 
Errors, 
Grouping.      Non-gr'ping. 
Prel.      Fin.      Prel.      Fin. 


64 
176 
62 
73 
42 
74 
85 
73 
89 
102 
29 
71 
48 
44 
50 
73 
77 
13 
58 


54 

88 

30 

131 

41 

57 

3S 

36 

50 

46 

34 

23 

3 

51 

39 

43 

42 

30 

55 

6 

0 

15 

7 

12 

13 

29 

2 

2 

3 

0 


50 
43 
46 
148 
43 
49 
11 
56 
58 
32 
92 
90 


60 
87 
35 
122 
45 
53 
29 
55 
61 
34 
51 
55 
19 
53 
31 
40 
14 
55 
46 
14 
23 
27 
41 
31 
25 
28 
12 
16 
8 


14 
9 
17 
14 
25 

3 

11 
4 
2 
2 
8 

17 
7 
9 
4 

21 
5 

12 
9 
S 
0 
2 
4 


20 

34 

10 

30 

34 

7 

0 

17 

4 

13 

16 

10 

G 

12 
4 
1 


21 
55 
27 
100 
37 
35 
11 


4 

12 
4 

22 
4 
5 
5 
5 

11 
5 

24 
4 
3 
5 
2 
0 
1 
5 
3 
6 
9 
1 

21 
5 

10 
6 
S 
0 
2 
3 


Totals: 


200 


1772 


160 


980 


1246        120 


282 


728        109 


747 


195 


COMPARISON:     I.    OF  SPELLINGS. 

GROUP  A   (28  Pupils). 
Preliminary. 

Total   words  to  spell 5600 

Total    words   mispelled 1772 

Average  mispelled  per  pupil 63.3 

Standing  of  class 68.36% 


97.14% 


GROUP  B  (22  Pupils). 


Final. 

Preliminary. 

Final. 

5600 

4400 

4400 

160 

1177 

282 

5.7 

53.5 

12.8 

■z.ion 


93.6% 


That  is.  Class  A  rose  from  68.36%  in  the  preliminary  to 
97.14%  in  the  final  test,  and  Class  B  rose  from  73.25%  in  the 
preliminary  to  93.6%  in  the  final  test. 


!5 


Class 
A 

C 

97.14 


936 


68.36 


73.25 


Linear  Representation  ol  Results 

The  results  of  the  tests  as  expressed  in  percent- 
ages are  here  shown  in  lines  drawn  on  a  similar  scale. 

Point  B  in  each  line  represents  the  percentage 
made  in  the  Preliminary  Test ;  point  C  represents  the 
percentage  made  in  the  Final  Test ;  distance  B  C 
shows  the  gain  made  by  each  class. 

Improvement  for  each  class  must  be  measured 
from  point  B.  Class  A  began  its  improvement  lower 
and  ended  higher,  a  fact  thus  made  clear  and  con- 
spicuous to  the  eye. 


No  method  of  computing  the  gain  having  heretofore  been  pro- 
posed, the  following  plan  of  comparison  and  computation  is 
adopted.  As  far  as  known,  the  two  classes  represent  approxi- 
mately children  of  the  same  average  ages  and  of  the  same  rela- 
tive school  advantages.  It  would  seem  therefore  as  if  Class  B, 
having  reached  a  higher  mark  in  the  preliminary  test,  must  repre- 
sent the  better  acquisitive  power,  in  the  ratio  of  73.25  to  68.36. 

According  to  the  preliminary  test,  again,  Class  A  had  100% 
minus  68.36%,  or  31.64%  to  learn;  in  the  same  way,  Class  B  had 
but  26.75%  to  learn.  Here,  then,  is  another  inequality,  and  it 
seems  as  if  the  chances  of  learning  must  be  in  proportion  to  the 

16 


quantity  to  be  learned,  or  as  if  Class  A's  chances  of  learning  were 
to  Class  B's  as  31.64  to  26.75.  This  ratio  appears  warranted  by 
the  consideration  of  the  fact  that  all  the  children  study  all  the 
words.  Therefore  the  group  having  most  words  to  learn  has  the 
better  chance  to  make  gain  or  to  learn  words  and  to  spell  those 
words  correctly  in  the  final  test  which  were  misspelled  in  the  pre- 
liminary test.     Compounding  these  ratios,  we  get  that — 

Class  A's  rate  of  gain  should  be  to  Class  B's  rate  of  gain  as, 
68.36  to  to  73.25,  and  as  31.74  is  to  26.75.  If  we  now  assume 
that  B,  being  the  group  which  uses  the  usual  method,  has  a  rate  of 
gain  of  1,  we  get  a  compound  ratio  that — 

A      :      B  ::         A        :       B 

::     68.36      :     73.25 
X      :      1  ::     31.64      :     26.75 

which  worked  out  gives,  X  equals  1. 1,  meaning  that  the  rate  of 
gain  in  Class  A  must  be  1 . 1  times  as  great  as  that  of  Class  B  if  it 
is  to  show  equal  efficiency,  and  that  whatever  rate  of  gain  greater 
than  1.1  Class  A  may  show  represents  the  relative  efficiency  of 
grouping  as  a  factor  in  learning  to  spell. 

The  rate  of  gain  of  the  two  classes  might  be  shown  in  each  of 
several  ways,  such  as  the  percentage  of  improvement  in  the  final 
test,  if  the  preliminary  test  be  used  as  base,  or  in  terms  of  what 
seemed  unknown  in  the  preliminary  test.  The  latter  plan  is  used 
here  since  that  is  the  only  process  possible  if  a  class  start  with  an 
entirely  unknown  mass  of  facts.  To  adopt  the  "unknown  of 
the  preliminary  test''  as  the  basis  for  computing  rate  of  learning 
will  give  uniformity  between  investigations  where  parts  of  the 
matter  is  known  and  those  where  none  of  it  is  knowm. 

Class  A  had  31 .64%  of  the  original  list  to  learn  after  the  pre- 
liminary test,  Class  B  had  26.75%  to  learn.  As  already  shown 
Class  A  improved  its  standing  in  the  final  test  by  28.78%  ;  this  is 
a  rate  of  91%  of  its  unknown,  of  the  31.64%  unknown.  Class 
B.  improved  its  standing  by  20.35%,  or  at  the  rate  of  70%  of  its 
unknown.  A  mere  arithmetical  difference  here  would  show 
Class  A  doing  better  by  the  difference  between  91%,  A's  rate  of 
gain,  and  70%,  B's  rate  of  gain,  or  21%  larger  rate  of  gain  in 
favor  of  Class  A. 

If  the  initial  difference  between  the  classes,  as  already  pointed 
out  and  equated  in  the  proportion  of  an  earlier  paragraph  be 
valid,  however,  we  should  compare  the  classes  with  all  possible 
inequalities  eliminated.  That  proportion  gave  us  the  ratio  of 
1 . 1  rather  than  as  absolute  equality,  and  means  that  to  do  as 
well  as  Class  B,  Class  A  must  show  a  rate  of  gain  at  least  1 . 1 
times  that  of  Class  B.  Now,  Class  B's  rate  of  gain  was  70%. 
Therefore  to  do  as  well  as  Class  B,  Class  A  must  make  1.1  times 
70%,  or  jyc/c  of  its  unknown.     Class  A  learned  91%  of  its  un- 

17 


known,  which  is  14%  better  than  77%,  and  which  is  just  20% 
of  B's  own  rate  of  gain  better  when  all  inequalities  have  been 
eliminated. 

To  learn  words  grouped  according  to  similarity  of  difficulty  in 
spelling  thus  seems  about  20%  better  than  the  usual  way, 
whether  the  advantage  be  computed  as  an  arithmetical  ratio  or  as 
an  arithmetical  difference.  If  this  single  factor  of  word-group- 
ing thus  adds  20%  to  the  efficiency  of  teaching  of  spelling,  it 
should  certainly  be  included  in  the  arrangement  of  spelling  lessons 
of  all  kinds.  Joining  this  unmistakable  advantage  as  thus  shown 
by  the  comparison  of  the  tests  to  what  was  so  clearly  foreshad- 
owed by  the  daily  lessons,  it  seems  proved  that— 

The  study  of  words  arranged  into  groups  according  to 
similarity  in  spelling  difficulty  is  20  per  cent.  better 
than  the  usual  non-grouping  method  of  arrangement 
and  study. 

II.    COMPARISON  OF  ERRORS. 

CLASS  A  (28  Pupils)  (LASS  B  (22  Pupils). 

Preliminary  Test.                 Final  Test.  Preliminary  Test.  Final  Test. 

1.          2.          3.             1.          2.              3.  1.          2.           3.  1.           2.          3. 

Total     %  of    Av.        Total     %  of          Av.  Total    %  of      Av.  Total     %  of      Av. 

No.  of  whole    per       No.  of  whole          per  No.  of  whole    per  No.  of    whole    per 
errors.      No.    pupil,    errors.    No.         pupil,      errors.     No.    pupil,  errors.      No.  pupil. 

Grouping 980        44        35.            66        35.5           2.36  728        49        33.1  109        32.6        5 

Non-grouping..     1246        56        44.5        120        64.5           4.3  747        51        34.  195        49.0        9 

REDUCTION   OF  ERRORS  : 

CLASS  A  CLASS  B 

Grouping,  from  an  average  of  35  to  2.36,  or  93.3%    :     from  33.1  to  5,  or  85.  %; 

Non-grouping,  from  an  average  of  44.5  to  4.3,  or  90.4%    :     from  34.0  to  9,  or   73.5%; 

This  shows  the  reduction  per  pupil  for  each  class. 

The  fact  that  Class  A  had  44%  of  its  errors  of  the  grouping 
variety,  and  Class B  49%,  in  the  preliminary  test,  shows  that  the 
grouping  according  to  difficulty  had  been  made  quite  successfully. 
As  already  stated,  many  words  could  quite  properly  have  gone 
into  other  groups  of  this  set,  and  in  an  attempt  to  incorporate  this 
grouping  idea  into  the  arrangement  of  spelling  lessons  con- 
sisting of  words  grouped  according  to  spelling  difficulty  that  is 
what  must  be  done. 

The  grouping  errors  were  very  considerably  reduced  in  both 
classes;  this  shows  that  Class  B  must  quite  regularly  have 
pointed  out  the  group  difficulty  as  "the  place  where  you  are  likely 
to  make  a  mistake1'  while  preparing  to  study  the  words. 

In  Class  A  the  non-grouping  errors  increase  from  56%  in  the 
preliminary  to  64.57c  in  the  final  test,  which  shows  very  mark- 
edly the  good  effect  of  the  grouping  for  that  kind  of  errors,  and 
also  confirms  the  statement  that  words  having  more  than  one 
difficulty  must  be  studied  in  more  than  one  group.  In  Class  B 
the.  reverse  took  place.     The  non-grouping  errors  fell  from  5 1  % 

18 


to  49%.     Apparently,  the  plan  of  having  the  children  point  out 
the  difficulty  in  the  word  occasionally  brought  out  some  other 
than  the  group  difficulty.      The  testimony  of  the  teachers  cor- 
roborates this  indication.     This  comparison  by  errors  brings  out 
a  fact  which  may  be  of  great  importance  in  the  teaching  of  spell- 
ing, namely,  the  pedagogical  mistake  of  calling  a  word  wrong 
and  deducting  but  one  point  of  credit  for  each  misspelled  word, 
without  regard  to  whether  there  was  one  or  more  than  one  error 
in  the  misspelling*;     Long  standing  practice  and  custom  has  es- 
tablished it  as  the  right  way,  but  it  is  at  least  worth  asking, 
whether  the  desire  to  do  well  and  to  stand  well  in  spelling  would 
not  be  helped  if  the  pupil  knew  that  it  was  possible  to  lose  more 
than  one  point  for  a  misspelled  word  in  case  he  made  more  than 
one  mistake  in  it.     Great  difficulties  would  be  encountered  in  at- 
tempting to  apply  such  a  method,  as,  for  instance,  shall  we  count 
the  literal  or  the  phonic  errors  ?  or,  how  shall  we  count  omitted 
words  ?     It  seems  probable  that  to  count  each  word  wrong  as  one 
point  wrong  being  both  easy  to  apply  and  having  high  practical 
value,  may,  therefore,  be  tolerated.     Just  as  an  example  in  an 
arithmetic  test  may  be  right  "in  principle"  but  wrong  in  compu- 
tation, and  therefore  is  refused  full  credit,  so  it  would  seem  un- 
fair to  pupils  who  misspell  words  by  but  a  single  letter  to  suffer 
as  much  loss  of- credit  as  do  pupils  who  have  two  or  three  errors 
in  each  misspelled  word.     Because  the  problem  seems  difficult  is 
no  reason  for  dismissing  it,  however.     If  one  plan  of  marking 
and  counting  mistakes  will  arouse  a  more  earnest  and  a  higher 
pitch  of  effort  to  secure  sustained  excellence  in  spelling",  that 
method  should  be  developed  as  soon  as  possible.     The  act  of 
calling  the  attention  of  the  child  to  the  particular  difficulty  which 
the  word  presents  to  him  is  certainly  the  first  step  toward  helping 
him  conquer  that  difficulty.     It  is  doubtful  whether  we  do  that 
in  our  present  way  of  marking  and  counting  errors. 

III.     Incidental  Results. 

As  a  matter  of  curiosity  it  will  be  worth  while  to  state  that  four 
words  were  not  missed  in  either  test;  they  are  direction,  laugh, 
neighbor,  weight.  There  were  seven  words  not  missed  at  all  in 
the  first  test,  and  54  words  not  missed  at  all  in  the  final  test.  A 
remarkable  fact  came  to  light  in  tabulating  the  errors  for  the  final 
test.  It  was  discovered  that  in  both  classes  there  were  mis- 
spellings of  words  in  the  final  test  which  had  been  spelled  cor- 
rectly in  the  preliminary  test.  In  Class  A  there  were  53  such 
misspellings  and  in  Class  B  there  were  90  of  them.  Mere  mass 
statistics  could  not  have  disclosed  this  fact.  It  came  to  light  only 
when  a  record  was  compiled  showing  each  pupil's  work  for  each 
word  in  the  preliminary  and  in  the  final  test.  Just  what  is  the 
significance  of  this  fact? 

19 


Evidently  that  guessing  was  present  in  the  preliminary  test; 
that  the  28  pupils  guessed  right  on  53  words  in  the  preliminary, 
and  wrong  in  the  final ;  the  22  pupils  guessed  right  on  90  words 
in  the  preliminary  test,  and  and  wrong  in  the  final  test.  While  it 
may  Ik*  true  that  some  of  the  mistakes  in  the  final  may  have  been 
mistakes  of  incoordination,  yet  on  the  whole  the  figures  indicate 
the  error  that  may  creep  into  investigations  of  this  kind  by  as- 
suming, as  is  often  done,  that  ''the  errors  in  the  one  group  will 
offset  the  errors  in  the  other,"  or,  that  in  either  group  "the  correct 
and  incorrect  guesses  will  offset  each  other."  This  could  be 
true  only  in  cases  where  the  chances  of  error  and  of  correctness 
were  exactly  even.  That  is,  if  there  were  but  one  wrong  and  one 
right  way  to  spell  a  word.  Since  there  is  but  one  right  way,  and 
since  there  are  innumerable  possibilities  of  getting  it  wrong,  the 
'chances  are  very  uneven,  and  the  assumption  of  offset  is  not  to  be 
admitted.  Scientific  investigation  must  get  the  facts.  In  this 
investigation  the  28  children  averaged  a  trifle  less  than  2  right 
guesses  in  the  preliminary  test,  and  the  same  wrong  guesses  in  the 
final  test :  the  22  children  averaged  a  little  more  than  4  right 
guesses  in  the  preliminary  test  and  the  same  wrong  guesses  in  the 
final  test,  and  this  after  having  studied  the  words  rather  inten- 
sively. It  would  certainly  be  interesting  and  valuable  to  find 
what  would  appear  if  there  were  no  study  of  words  or  matter  be- 
tween two  tests. 

While  this  number  of  children  was  small,  only  fifty  in  all,  it 
does  not  seem  reasonable  to  suppose  that  it  would  equalize  itself 
if  the  number  were  larger,  say  1,000  or  10,000.  The  real  wrong 
of  the  assumption  is  not  that  an  equal  number  of  children  may  be 
uncertain  and  guess;  for  the  sake  of  the  argument  that  may  be 
conceded,  just  as  we  concede  the  insurance  man's  claim  that  so 
many  people  out  of  a  thousand  of  a  given  age  will  die  in  any  one 
year.  If  true,  however,  the  difficulty,  whether  in  spelling  or  in 
arithmetic,  comes  from  assuming  that  those  who  guess  or  en- 
have  just  as  many  chances  to  be  right  as  to  be  wrong  !The  chances 
of  error  are  greater  than  the  chances  of  right,  entirely  independ- 
ent of  the  number  of  children  that  do  the  guessing.  In  is  the  fact 
of  hundreds  of  chances  of  wrongness  to  the  one  chance  of  Tight- 
ness that  decides  the  matter  in  favor  of  error. 

XL     Words  Correctly  Spelled  in  the  Preliminary  Test 
but  Misspelled  in  the  Final  Test. 

The  table  showing  such  variation  in  misspelling  is  included  for 
reasons  that  will  appear  presently. 


20 


CLASS   A 


CLASS   B 


MISSPELLINGS. 

MISSPELLS 

In  the  Final  Test. 

Indi  . idual 

In  the  Final  Test. 

In  the 

Same  words         Different 

pupils  in 

In  the 

Same  words 

Different 

Preliminary 

as  in 

WO* 

Is  from 

numerical 

Preliminary 

as  in 

words  from 

Teat. 

Prelim.  Test.    Prel 

in. 

Test. 

order. 

Teat 

Prelim.  Test.     Prelim.  Test. 

7.-. 

3 

0 

1 

38 

4 

0 

74 

3 

0 

2 

30 

0 

0 

34 

2 

0 

3 

29 

2 

0 

30 

0 

, 

0 

4 

23 

0 

1 

7d 

2 

0 

5 

65 

7 

1 

54 

1 

0 

6 

29 

3 

1 

07 

2 

0 

7 

45 

3 

1 

65 

3 

8 

42 

2 

2 

51 

0 

9 

54 

3 

2 

48 

1 

10 

43 

7 

2 

71 

1 

11 

69 

12 

2 

70 

1 

12 

53 

4 

3 

24 

0 

13 

83 

8 

3 

38 

0 

14 

54 

10 

4 

21 

0 

15 

57 

4 

5 

66 

4 

10 

35 

4 

6 

54 

2 

17 

90 

23 

7 

63 

1 

2 

18 

95 

30 

8 

94 

3 

2 

19 

1     55 

15 

8 

69 

3 

2 

20 

65 

13 

9 

44 

2 

3 

21 

56 

22 

11 

82 

8 

4 

22 

65 

16 

14 

118 

17 

4 

23 

57 

11 

4 

24 

79 

5 

4 

25 

103 

16 

5 

26 

74 

2 

0 

27 

84 

12 

7 

28 

SUMMARY 

CLASS 

A 

CLASS 

B 

The 

X... 

of 

TOTAL 

MISSPELLINGS. 

No.  of 

TOTAL  MISSPELLINGS. 

several 

pupils 

Final  Test. 

pupils 

Final  Test. 

numbers  of 

mis- 

ing 

Prelim. 

Same 

Different 

missing 

Prel. 

Same 

Different 

diff.  errors. 

this 

No. 

Test. 

words. 

words. 

this  No. 

Test. 

words 

words. 

0 

7 

404 

13 

0 

3 

97 

6 

0 

1 

10 

514 

12 

10 

162 

13 

4 

2 

3 

256 

g 

6 

208 

24 

8 

3 

1 

44 

2 

3 

136 

12 

6 

4 

4 

333 

41 

16 

54 

10 

4 

5 

1 

103 

16 

5 

57 

4 

5 

6 

1 

74 

2 

6 

■     35 

4 

6 

7 

1 

81 

12 

7 

90 

23 

7 

8 

0 

150 

45 

16 

9 

0 

65 

13 

9 

11 

0 

56 

22 

11 

14 

0 

65 

16 

14 

AVERAGES 

FOB    EACH    GROUP   OF    "NUMBERS  OF 

DIFFFREXT  WORDS  MISSED  IX  FINAL": 

0 

7 

f.7.7 

1.9 

0 

32.3 

2.0 

0 

1 

10 

51.4 

1.2 

1 

40.T) 

3.3 

1 

2 

3 

85.3 

3.0 

2 

52.0 

6.0 

2 

3 

1 

44.0 

2.0 

3 

68.0 

6.0 

3 

4 

4 

83.3 

10.3 

4 

54.0 

10.0 

4 

6 

1 

103.0 

16.0 

5 

57.0 

4.0 

5 

6 

1 

74.0 

2.0 

6 

35.0 

4.0 

6 

7 

1 

84.0 

12.0 

7 

90.0 

23.0 

7 

8 

0 

0 

0 

0 

2 

75.0 

22.5 

8 

FURTHER   CONSIDERATION    OF   THE   VARIATION. 

There  seems  no  discoverable  relation  l)etween  initial  correct 
spelling-  and  the  likelihood  of  misspelling-  words  in  the  final  test 
that  were  not  misspelled  in  the  preliminary  test,  which  shows  the 


21 


presence  of  the  factor  of  guessing.  It  might  be  supposed  that  the 
poorer  spellers  do  most  guessing,  but  the  records  hardly  bear  out 
this  supposition.  Thus,  pupils  No.  2  and  No.  27  in  class  A  both 
misspelled  74  words  in  the  preliminary  test.  Pupil  No.  2  missed 
none  in  the  final,  but  pupil  No.  27  missed  8  in  the  final,  6  of 
which  he  had  not  missed  in  the  preliminary  test.  Pupil  No.  2 
certainly  did  less,  or  perhaps  better,  guessing  than  pupil  27. 
Again,  the  group  missing  6  different  words  in  Class  B  had  an 
average  misspelling  of  but  35  words  in  the  preliminary  test, 
which  was  the  next  to  the  lowest  average  of  any  group  in  either 
class,  and  very  much  lower  than  the  o  group  in  Class  A,  which 
had  an  average  of  57.7  in  the  preliminary  test. 

The  chances  of  correct  guessing  and  of  incorrect  guessing  in 
such  work  as  this  can  be  worked  out  actually  for  these  two  groups 
of  children.  In  Class  A,  7  pupils  missed  only  words  in  the  final 
which  had  also  been  missed  in  the  preliminary,  and  21  missed  dif- 
ferent words  in  the  final.  Correct  guessing,  if  present,  seems  to 
have  hit  it  in  proportion  of  1  to  3.  The  21  pupils  missed  53  such 
words,  or  an  average  of  2.52  errors  per  pupil.  If  among  the 
pupils  the  proportion  was  1  to  3,  and  each  pupil  making  an  error 
made  2.52  errors,  the  chances  of  correct  to  incorrect  guessing 
that  actually  materialized  here  were  3  times  2.56  or  7.68  to 
every  correct  guess.  In  Class  B,  the  chances  among  the  pupils 
are  3  correct  to  19  incorrect,  or  6.33;  now  the  19  pupils  missed 
90  words,  an  average  of  4.74  words  each.  Since  6.33  times 
4.74  equals  just  about  30,  we  have  here  30  chances  of  error  to  1 
of  correctness  that  is  actually  realized.  Thus  the  assumption  of 
correct  and  incorrect  guessing  on  the  part  of  contrasted  groups  of 
children,  or  between  contrasted  methods,  is  shown  to  be  entirely 
untrustworthy  and  unscientific.  The  incorrect  guesses  of  the 
one  group  certainly  did  not  offset  those  of  the  other.  The  Class 
B,  which  were  the  better  spellers  at  the  start,  make  almost  twice 
as  many  such  errors  as  Class  A.  Incidentally,  this  constancy, 
whether  positive  knowledge  or  merely  a  keener  guessing  power, 
seems  to  further  show  the  advantage  of  the  grouping  method  of 
study,  since  Class  A  had  much  the  smaller  percentage  of  such 
errors. 

XII.     Validity  of  Preliminary  Test. 

This  variation  very  certainly  casts  doubt  on  the  absolute  de- 
pendence upon  the  results  of  the  preliminary  test  as  measuring 
the  point  from  which  advance  is  made.  If  the  preliminary  tc^ts 
were  corrected  for  each  of  the  two  classes,  Class  A  would  lose 
1%  of  its  preliminary  standing,  and  Class  B  about  3%.  No 
correction  of  the  results  has  been  made  to  incorporate  these  va- 
riations.    The  final  test  would  certainly  show  some  variations, 

22 


therefore  the  results  are  presented  with  this  mere  statement  of  the 
fact  that  a  trifling  variation  is  present.  This  is  probably  the  as- 
tronomer's "personal  equation."  It  may  be  of  value,  however, 
to  suggest  that  some  future  investigation  should  be  made  to  as- 
certain, if  possible,  what  is  the  percentage  of  variation  that  must 
be  allowed  in  preliminary  tests.  It  is  of  course  greater  than  in 
hnal  tests  after  teaching  and  drill  on  a  subject.  Its  approximate 
value  can  be  determined  by  several  trials  of  a  test  with  the  same 
groups  of  children,  and  will  be  a  valuable  factor  to  know  in  all 
experimental  pedagogical  work. 

XIII.     The  Efficacy  of  the  Respective  Groups  of  Words. 

Besides  the  value  which  this  investigation  may  have  in  the  light 
it  throws  upon  "grouping  vs.  non-grouping"  as  a  method  of 
study,  an  analysis  of  the  effectiveness  of  the  several  kinds  of 
grouping  here  resorted  to  may  be  of  value  in  suggesting  the 
kinds  of  grouping  to  use  in  the  method,  since  not  all  the  groups 
appear  to  have  been  equally  effective.  Therefore,  the  following 
table  of  results  in  Class  A,  the  children  who  studied  by  the  group- 
ing method,  will  indicate  whatever  efficacy  any  group  had. 

THE  COEFFICIENT  OF   EFFICIENCY  OF  GROUPING. 

It  seemed  desirable  to  compare  the  respective  groups  with  each 
other  as  to  efficiency ;  to  do  so,  a  standard  must  be  fixed,  and  a 
method  of  comparison  worked  out  which  should  resolve  itself 
into  a  single  amount  or  number,  indicating  efficiency  as  com- 
pared with  the  standard  group.  Since  original  and  final  status 
should  appear  in  the  computation,  the  following  method  of  com- 
puting the  coefficient  was  decided  upon. 

An  inspection  of  the  entire  30  groups  showed  two  very  de- 
sirable qualities  inherent  in  the  results  for  group  17.  First,  it  is 
almost  the  methematical  median  of  the  entire  30,  and  second,  in 
the  final  test  all  its  words  were  spelled  correctly,  so  that  its  effi- 
ciency is  100'.  .  which  means  that  all  was  learned  that  could  be 
learned  in  that  group.  This  group  having  been  fixed  upon  for 
the  standard,  the  average  number  of  misspellings  of  the  words  in 
the  group  in  the  preliminary  test  was  found,  and  it  was  8.33: 
this  then  was  treated  as  the  standard  of  difficulty  of  the  words, 
and  the  comparative  difficulty  of  the  words  in  any  other  group, 
for  these  28  children,  of  course  (and  not  for  the  world  in  gen- 
eral) was  found  by  dividing  the  average  misspellings  in  any 
other  group  by  this  8.33.  Thus,  group  2  it  will  be  seen  has  an 
average  of  16.5  misspellings,  which  means,  according  to  the 
comparison  here  proposed,  that  the  words  of  group  2  were  twice 
as  difficult  at  the  start  as  those  of  the  standard  group — group  17: 
I  his  becomes  one  factor  of  the  coefficient  of  efficiency. 

23 


Next,  the  percentage  of  improvement  in  each  group  must  be 
compared  with  the  percentage  of  improvement  in  the  standard 
group:  out  of  these  comparisons,  a  compound  proportion  grows 
which  is  easily  resolvable,  and  workable  by  a  simple  rule.  Group 
2  showed  an  improvement  of  goc/c ,  and  if  we  compare  groups 
17  and  2  we  get  this  proportion: 

Av.  Misspell.  Improvement. 

Group     2 16.5  .90% 

"        17 8.33  100% 

If  group  17  be  now  called  an  efficiency  of  I,  what  efficiency  has 
group  2  shown  ?  .  Here  is  the  answer : 


1  : 


16.5 

90. 

2  :  1 


8.33 

100,  which  may  be  simplified  into  this- 


.9:1,  which  yields  us  the  result — 
x  =  1 . 8,  as  the  efficiency  of  group  2,  and  also  the  simple 

rule  that  degree  of  difficulty  multiplied  by  the  decimal  ratio  of 
their  percentages  of  improvement  will  yield  the  coefficient  of  effi- 
ciency. It  is  by  this  method  and  by  this  rule  that  the  coefficients 
of  the  following  table  were  computed  : 


AVERAGE 

MISSPELLING. 

Gain. 

Coefficient 

Group. 

Preliminary. 

Final. 

% 

of  efficient'; 

1 

19.5 

1.00 

94.84 

2.22 

2 

16.5 

1.80 

90. 

1.79 

3 

16. 

1.75 

78. 

1.5 

4 

16. 

1.98 

88.2 

1.7 

5 

15.5 

1.75 

89. 

1.66 

6 

14.6 

1.8 

87.6 

1.53 

7 

14. 

2. 

86. 

1.42 

8 

12.5 

.5 

96. 

1.44 

9 

'     12.14 

1.4 

93. 

1.36 

10 

11.85 

1.2 

93. 

1.32 

11 

10.38 

1.25 

87.95 

1.09 

12 

10.2 

.8 

92.15 

1.13 

13 

9.7 

.75 

86.2 

1.01 

14 

8.87 

1.33 

91.7 

1.56 

15 

8.8 

.4 

95.5 

1.53 

16 

8.8 

.00 

100. 

1.06 

17 

8.33 

.00 

100. 

1. 

18 

8.11 

1.00 

87.52 

.85 

19 

7.7 

1. 

78. 

.72 

20 

6.5 

.5 

92.3 

.72 

21 

6.45 

1.11 

•    86.1 

.66 

22 

6. 

.00 

100. 

.72 

23 

5.6 

.5 

78.1 

.52 

24 

5.11 

.22 

96. 

.58 

25 

4.8 

1.2 

75. 

.43 

26 

4.63 

.7 

98.65 

.55 

27 

4.14 

.43 

89.9 

.45 

28 

1.75 

.25 

•       87. 

.18 

29 

1.4 

.2 

86. 

.13 

30 

1.33 

.33 

75. 

.12 

It  may  be  of  interest,  and  even  of  added  value,  that  the  group 
chosen  as  standard  has  an  average  of  misspellings  almost  equal 

24 


to  that  of  the  average  of  misspellings  of  the  entire  list,  which  is 
.  or  just  about  the  same  as  group  14. 

It  appears  that  both  the  most  and  the  least  effective  group  is 
etymological,  that  is  group  1,  with  a  coefficient  of  2.22,  and 
group  30  with  a  coefficient  of  .12.  Groups  18  and  21  offer  a 
striking  contrast:  Group  18,  the  nouns  ending  in  "y/1  singular, 
preceded  by  a  consonant,  for  whose  spelling  there  is  an  easy  rule, 
is  .85,  and  for  group  21.  the  singulars  of  the  same  nouns,  for 
whose  spelling  there  is  no  rule,  the  coefficient  is  but  .66.  Seem- 
ingly, here  is  another  corroboration  in  favor  of  the  study  by 
grouping  according  to  spelling  difficulty. 

The  size  of  the  groups  seems  to  have  had  little  or  nothing  to  do 
with  the  efficiency:  group  4,  with  1 1  words,  is  more  efficient  than 
group  5.  with  4  words.  The  etymological  groups  clearly  do  not 
show  a  marked  higher  efficiency,  for  they  are  found  scattered 
quite  evenly  throughout  the  table,  in  places  1,  3,  10,  12,  17,  20,  28, 
30.  Since  most  of  the  other  groups  were  phonetic  or  the  equiva- 
lent of  phonetic,  the  same  conclusion  must  be  drawn  for  that 
kind  of  grouping.  It  seems  probable,  however,  that  with  older 
pupils  there  might  have  been  evidence  of  higher  efficiency  of  the 
etymological  grouping,  since  that  appeals  to  reasoning  as  well  as 
to  analogy  of  literal  form.  In  sixth  grade  children  this  form  of 
comparison  and  association  is  just  beginning  to  show  itself.  The 
earlier  habits  of  the  children  were  at  least  as  strong  as  the  factor 
which  the  investigation  was  bringing  consciously  into  opera- 
tion in  their  study.  Group  26,  the  largest  group  in  the  lot,  con- 
taining 16  words,  is  near  the  end  of  the  list,  with  an  efficiency  of 
Group  2^.  with  12  words,  shows  an  efficiency  of  but  .52. 
In  both  cases,  however,  it  is  not  the  size  of  the  group,  but  the  in- 
effective grouping  that  is  the  cause.  In  both  groups,  the  group- 
ing errors  are  but  a  small  part  of  the  actual  errors,  which  once 
again  emphasizes  the  necessity  of  including  the  same  word  in 
different  groups  according  to  the  number  of  difficulties  of  actual 
spelling  which  it  contain^. 

XIV.     Sum  mar  v. 

1.  Preliminary  Tests  are  not  absolutely  but  only  approximately 
correct  as  a  point  from  which  to  measure  improvement  due  to  a 
method  of  instruction. 

2.  Grouping  words  into  lessons  according  to  spelling  difficulty 
is  better  than  the  ordinary  plan  of  spelling  lessons.  It  secures 
better  daily  lessons,  better  final  results,  and  greater  steadiness  or 
constancy  of  correct  spelling, 

3.  Computation  of  gain  or  improvement  should  be  upon  the 
is  of  the  "unknown"- in  the  preliminary  test,  so  as  to  secure 

comparable  results  from  all  experimental  investigations. 

25 


4.  A  word  should  be  grouped  with  as  many  separate  groups  as 
it  contains  real  spelling  difficulties.  In  any  one  group  this 
focuses  the  attention  upon  but  one  difficulty,  making  mastery  of 
that  more  probable,  and  in  the  end  all  its  difficulties  will  be  mas- 
tered. 

5.  It  is  not  safe  to  assume  that  variations  to  right  and  wrong 
"offset"  each  other  in  large  numbers  of  children,  unless  the 
chances  of  error  and  of  correctness  are  exactly  equal.  Where 
the  chances  of  error  outnumber  the  chances  of  correctness,  even  if 
the  average  number  of  guesses  on  the  two  sides  be  equal,  the 
errors  will  outnumber  the  correct  variations. 

6.  Grouping  shows  its  effectiveness  by  every  test  to  which  we 
submit  the  figures,  even  among  the  groups  themselves. 

7.  A  coefficient  of  efficiency  for  the  matter  of  instruction  can 
be  found  by  adopting  a  standard  mass  or  unit,  and  then,  through 
the  results  of  a  preliminary  test,  ascertain  the  relative  difficulty 
of  other  units  or  masses,  and  multiply  this  ratio  of  difficulty  by 
the  ratio  of  improvement  between  the  standard  mass  or  unit  and 
any  other  unit,  as  shown  by  the  final  test. 

8.  Is  our  present  plan  of  counting  each  misspelled  word  as  but 
one  wrong,  regardles  of  the  number  of  errors  it  may  contain, 
conducive  to  the  highest  efficiency  of  method  in  spelling?  Would 
not  the  counting  of  the  actual  errors,  by  calling  attention  to  each 
error  specifically,  result  in  having  most  effort  applied  at  the  point 
of  greatest  resistance  ? 

9.  A  method  is  proposed  to  equate  original  difference  of  groups 
of  children,  so  as  to  secure  a  basis  for  comparison  of  contrasted 
methods.  The  rates  of  gain  should  be  to  teach  each  other  as  the 
percentages  of  standing  in  the  preliminary  test,  and  also  as  the 
percentages  of  "unknown"  in  the  preliminary  test.  Equating  the 
percentages  of  the  preliminary  test  equalizes  acquiring  power,  and 
equating  the  unknown  of  the  preliminary  test  equalizes  the  chances 
of  learning.  This  applies  only  to  tests  where  the  entire  field  or 
body  of  matter  comprehended  in  the  preliminary  test  is  also  cov- 
ered in  the  teaching  or  learning  of  the  two  contrasted  groups. 
This  method  of  computing  enables  us  to  show  what  one  class 
should  do  in  terms  of  the  other,  thus  giving  us  a  ratio  of  com- 
parison before  final  results  are  known.  Prediction  of  the  result 
thus  becomes  possible  with  a  high  degree  of  probability  of  its 
approximate  tendency  in  the  right  direction. 

10.  The  Study  of  Words  arranged  into  Groups  accord- 
ing TO  SIMILARITY  IN  SPELLING  DIFFICULTY  IS  20  PER  CENT. 
BETTER  THAN  THE  USUAL  NON-GROUPING  METHOD  OF  ARRANGE- 
MENT AND  STUDY. 


26 


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